Question

Question 1. [7 marks total] Parental leave is often compensated to some degree, but the amount of compensation varies greatly. You read a research article that stated, "across people of all incomes, 47% of leave-takers received full pay during their leave, 16% received partial pay, and 37% received no pay." After reading this, you wonder what the distribution of parental leave payment pay is for low income households. Suppose you conduct a survey of leave-takers within households earning less than $30,000 per year. You surveyed 225 people (selected in a random sample) and found that 51 received full pay, 33 received partial pay, and 141 received no pay.

1.d) [2 marks] Compute the p-value for your test statistic and conclude whether
you believe there is evidence against the null hypothesis in favor of the alternative
hypothesis.

Answer 1

Null hypothesis :H_o :Distribution of parental leave payment pay matches with the given distribution,

Alternate hypothesis :H_a Distribution of parental leave payment pay does not match with  the given distribution,

Chi-square test for Goodness of fit is appropriate to test this.

Given,

	Observed counts
Full pay	51
Partial Pay	33
No pay	141
Total	225

Distribution of parental leave payment pay:

% leave-takers received full pay during their leave : 47%

%  received partial pay : 16%

% received no pay : 37%

Expected counts :

Expected Number of people - full pay = 47% of 225 = (225x47)/100 = 105.75

Expected Number of people - Partial pay = 16 % of 225 = (225x16)/100 = 36

Expected Number people - No pay = 37% of 225 = (225x37)/100 = 83.25

	Observed counts	Expected Counts
Full pay	51	105.75
Partial Pay	33	36
No pay	141	83.25
Total	225	225

Test Statistic :

	Observed counts	Expected Counts	O-E	(O-E)2	(O-E)2/E
Full pay	51	105.75	-54.75	2997.5625	28.3457
Partial Pay	33	36	-3	9	0.25
No pay	141	83.25	57.75	3335.0625	40.0608
Total	225	225			68.6566

Degrees of freedom : Number of categories - 1 = (3-1)=2

For 2 degrees of freedom :

As p-value : 0.0000 < :level of significance (either 0.1,0.05 or 0.001; or any) ; Reject the null hypothesis.

There is evidence against the null hypothesis in favor of alternative hypothesis.